Dual-scale structure optimization design method and system based on substructure data driving

Abstract

The invention belongs to the related technical field of dual-scale structure design, and discloses a dual-scale structure optimization design method and system based on substructure data driving, and the method comprises the steps: an offline stage: for cell elements of a dual-scale structure, carrying out the cutting operation of a level set function, obtaining a virtual microstructure, and carrying out the cutting operation of the level set function; determining the density of the actual microstructure according to the density of the virtual microstructure; performing static condensation through a substructure method to obtain a stiffness matrix of the super-unit, and constructing a mapping model of the cutting height parameter, the stiffness matrix of the super-unit and the density of the actual microstructure; in the online stage, a data driving model with the cutting height parameter as the input quantity and the stiffness matrix of the super-unit and the density of the actual microstructure as the output quantity is obtained; and applying the data driving model to a finite element optimization process of the dual-scale structure, and finally obtaining an optimized dual-scale structure. According to the invention, an off-line data driving method is adopted to carry out dual-scale structure optimization, and the efficiency can be greatly improved under the condition that the precision is ensured.

Description

Technical Field

[0001] The present invention belongs to the technical field related to dual-scale structure design, and more specifically, relates to a dual-scale structure optimization design method and system based on substructure data driving. Background Art

[0002] The dual-scale structure has both macroscale and microscale. It can not only change the mechanical properties of the entire macroscale by changing the shape of the microscale, but also has the advantages of high specific strength and high specific stiffness. The dual-scale structure has a wide range of application scenarios in the aerospace, mechanical and medical fields. For example, some support structures in space shuttles or mechanical equipment, or medical bones, can be set as dual-scale structures to improve support performance.

[0003] At present, there are design problems in dual-scale structural optimization methods. Dual-scale optimization based on scale separation methods such as homogenization method needs to consider the connectivity between microstructures; substructure method based on scale association can ensure the connectivity between microstructures, but the traditional substructure method needs to re-condense and calculate the stiffness matrix of each super unit in each optimization iteration, which is very time-consuming, resulting in low overall calculation efficiency. Existing methods based on scale association such as multi-scale finite element method and substructure method have the problem of time-consuming calculation. Summary of the invention

[0004] In response to the above defects or improvement needs of the prior art, the present invention provides a substructure data-driven dual-scale structure optimization design method and system, which is used to solve the problem of time-consuming calculation in the existing dual-scale structure optimization method based on scale association.

[0005] To achieve the above object, according to one aspect of the present invention, a dual-scale structural optimization design method based on substructure data driving is provided, comprising:

[0006] Offline data processing stage:

[0007] S1, for the cells in the design domain of the dual-scale structure, the virtual microstructure is obtained by cutting the level set function, the density of the actual microstructure is determined according to the density of the virtual microstructure, and the dual-scale structure is described by the actual microstructure;

[0008] S2, according to the density of the actual microstructure of the cell, static condensation is performed through the substructure method to obtain the stiffness matrix of the super unit formed after the cell is condensed, and a mapping model of the cutting height parameter in the cutting operation, the stiffness matrix of the super unit and the density of the actual microstructure is constructed;

[0009] Online optimization design stage:

[0010] S3, obtaining a data-driven model with a cutting height parameter as an input quantity and a stiffness matrix of a super-element and a density of an actual microstructure as an output quantity according to the mapping model;

[0011] S4, taking the cutting height parameters of each cell in the design domain of the dual-scale structure as the design variables, the volume fraction as the constraint condition, and the minimum flexibility as the objective function, an optimization model of the dual-scale structure is established; finite element analysis is performed on the optimization model, and in each iteration, the stiffness matrix output by the data-driven model is used to calculate the sensitivity of the flexibility to the cutting height parameter, and the density output by the data-driven model is used to calculate the sensitivity of the volume fraction to the cutting height parameter, and the cutting height parameter is iteratively optimized according to the sensitivity to finally obtain the optimized dual-scale structure.

[0012] According to the substructure data-driven dual-scale structural optimization design method provided by the present invention, S1 specifically includes:

[0013] For cells in the design domain of the dual-scale structure, multiple level set functions are selected, and multiple cutting operations are performed on each level set function to form multiple cutting height combinations. Each cutting height combination includes multiple cutting heights corresponding to the multiple level set functions. Multiple virtual microstructures corresponding to the multiple level set functions under each cutting height combination are obtained, and the multiple virtual microstructures are converted into density expressions and the max value is taken to obtain the density of the actual microstructure under each cutting height combination.

[0014] Correspondingly, the cutting height parameters in S2, S3 and S4 are cutting height combinations of various virtual microstructures.

[0015] According to the dual-scale structural optimization design method based on substructure data driving provided by the present invention, the density of the actual microstructure in S1 is obtained according to the following formula:

[0016] Using the level set function and cutting height Represents the combined function obtained by a cutting operation

[0017]

[0018] Wherein, D is the design domain; k is the number of cells, M is the total number of cells, and N is the number of virtual microstructures;

[0019] The part where the combination function is less than 0 is defined as a virtual microstructure Get virtual microstructure for:

[0020]

[0021] Convert virtual microstructure into density results And perform the max operation to get the actual microstructure Ω k The density result ρ k :

[0022]

[0023] Finally, the actual microstructure is used to represent the dual-scale structure Ω:

[0024]

[0025] According to the dual-scale structural optimization design method based on substructure data driving provided by the present invention, the stiffness matrix of the super unit in S2 is obtained in the following way:

[0026] First, according to the substructure method, the node degrees of freedom of the cell are reordered, and the appropriate node degrees of freedom are divided into internal node degrees of freedom and boundary node degrees of freedom. The finite element equilibrium equation of the cell is transformed into:

[0027]

[0028] Among them, K bb is the substructure stiffness matrix corresponding to the boundary node; K bi and K ib is the substructure stiffness matrix of the substructure boundary nodes and internal nodes coupled to each other; K ii is the substructure stiffness matrix corresponding to the internal nodes; U b is the displacement vector of the substructure boundary node; U i is the displacement vector of the node inside the substructure; F b is the external force vector of the substructure boundary node; F i is the external force vector of the internal node of the substructure;

[0029] Then, the finite element equilibrium equation of the super-element is obtained by static condensation:

[0030] K r U r =F r ;

[0031] Since all selected external points are retained during the condensation process, namely U r =U b , we can get:

[0032]

[0033]

[0034] Among them, K r is the stiffness matrix of the superelement; U r is the superelement displacement vector; Fr is the superelement external force vector.

[0035] According to the substructure data-driven dual-scale structural optimization design method provided by the present invention, S3 specifically includes:

[0036] The mapping model is interpolated using a compactly supported radial basis function interpolation technique to obtain the data driven model.

[0037] According to the dual-scale structural optimization design method based on substructure data drive provided by the present invention, the stiffness matrix of the super unit and the density of the actual microstructure are obtained by solving the compact support radial basis function interpolation formula and the mapping model as follows:

[0038]

[0039] in, is the stiffness matrix obtained by interpolation; i = 1…N, N is the number of virtual microstructures; n is the number of node degrees of freedom of the super-element after condensation; V H is the volume obtained by interpolation; α is the expansion coefficient of the compactly supported radial basis function; φ(r) is the radial basis function; r is the distance from the interpolation point to the center point; p i represents the coordinate center point of the interpolation function; x here represents the cutting height combination of various virtual microstructures in the cell; τ is the free shape parameter; d s A custom constant.

[0040] According to the dual-scale structural optimization design method based on substructure data drive provided by the present invention, the optimization model in S4 is specifically:

[0041]

[0042] Where i represents the type of virtual microstructure; c is the flexibility; V is the volume; is the volume value of the constraint; U is the global displacement vector; F is the global external force vector.

[0043] According to the dual-scale structural optimization design method based on substructure data driving provided by the present invention, the sensitivity of flexibility to the cutting height combination can be expressed as:

[0044]

[0045] According to the compactly supported radial basis function interpolation formula, we can It is expressed as:

[0046]

[0047] The sensitivity of volume fraction to the combination of cut heights is expressed as:

[0048]

[0049] Where V is the volume of the dual-scale structure; ρ k is the density of the actual microstructure corresponding to the kth cell; M is the total number of cells.

[0050] According to the substructure data-driven dual-scale structure optimization design method provided by the present invention, the optimized dual-scale structure obtained in S4 specifically includes:

[0051] Finite element analysis is performed on the optimization model to calculate the sensitivity of flexibility to the cutting height combination, the sensitivity of volume fraction to the cutting height combination, and the moving asymptote method is used to update the cutting height combination;

[0052] When the updated structural flexibility error meets the preset optimization termination condition, the optimization analysis is completed and the optimized dual-scale structure is obtained.

[0053] According to another aspect of the present invention, a dual-scale structure optimization design system based on substructure data driving is provided, the system includes a memory and a processor, the memory stores a computer program, and the processor executes any of the above-mentioned dual-scale structure optimization design methods based on substructure data driving when executing the computer program.

[0054] In general, compared with the prior art, the above technical solutions conceived by the present invention provide a dual-scale structural optimization design method and system based on substructure data drive:

[0055] 1. The actual microstructure of each cell in the dual-scale structure is used to form the final dual-scale structure, which can be conveniently used to determine the density of the actual microstructure according to the density of the virtual microstructure formed by the cutting level set function; according to the density of the actual microstructure, a large number of super-unit stiffness matrices can be directly generated by static condensation using the substructure method to form an offline database, i.e., a mapping model, and a data-driven model that meets the accuracy is constructed according to the database. The data-driven model can be used to obtain the stiffness matrix parameters and volume parameters required for the iterative optimization process to complete the structural optimization design. The present invention adopts an offline data-driven method to perform dual-scale structure optimization, and the dual-scale structure optimization under data-driven can greatly improve the efficiency while ensuring the accuracy;

[0056] 2. The mapping model is obtained based on the substructure method, that is, through the dual-scale structural optimization driven by substructure data, it can reduce the time cost while ensuring good microstructure connection, and obtain an optimization result with better flexibility and larger design space;

[0057] 3. It is proposed that the actual microstructure is expressed by density, and the stiffness matrix of the super unit is obtained by static condensation. The mapping model established by using the cutting height parameter, the stiffness matrix of the super unit and the density of the actual microstructure enables the constructed data-driven model to directly output the stiffness matrix and density, i.e., volume, according to the cutting height parameter, which is directly used for calculation in the iterative optimization process, making the calculation process simpler and more direct, which is conducive to improving the calculation effect and accuracy.

[0058] 4. Taking maximizing structural stiffness as the design goal and the volume of the overall structure as the constraint condition, the moving asymptote method is used to update the design variables until the optimization termination condition is met to obtain the optimal dual-scale structure. The present invention can ensure the connectivity of the microstructure in the overall structure, greatly improve the optimization efficiency and obtain the optimal material distribution. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a structural schematic diagram of a cantilever beam dual-scale structural optimization design provided by an embodiment of the present invention;

[0060] Figure 2 It is a microstructure model of four virtual microstructures in each cell of the dual-scale structure provided by an embodiment of the present invention when the cutting height is 0.5;

[0061] Figure 3 is a schematic diagram of a super unit obtained after static condensation of substructures provided in an embodiment of the present invention;

[0062] Figure 4 is a flow chart of a dual-scale structural optimization design method based on substructure data drive provided by an embodiment of the present invention;

[0063] Figure 5 This is the optimization result of the dual-scale structure when the method provided by the embodiment of the present invention is adopted. DETAILED DESCRIPTION

[0064] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0065] See also Figure 1 and Figure 4 , this embodiment 1 provides a dual-scale structure optimization design method based on substructure data driving, the method comprising:

[0066] Offline data processing stage:

[0067] S1, for the cells in the design domain of the dual-scale structure, the virtual microstructure is obtained by cutting the level set function, the density of the actual microstructure is determined according to the density of the virtual microstructure, and the dual-scale structure is described by the actual microstructure;

[0068] S2, according to the density of the actual microstructure of the cell, static condensation is performed through the substructure method to obtain the stiffness matrix of the super unit formed after the cell is condensed, and a mapping model of the cutting height parameter in the cutting operation, the stiffness matrix of the super unit and the density of the actual microstructure is constructed;

[0069] Online optimization design stage:

[0070] S3, obtaining a data-driven model with a cutting height parameter as an input quantity and a stiffness matrix of a super-element and a density of an actual microstructure as an output quantity according to the mapping model;

[0071] S4, taking the cutting height parameters of each cell in the design domain of the dual-scale structure as the design variables, the volume fraction as the constraint condition, and the minimum flexibility as the objective function, an optimization model of the dual-scale structure is established; finite element analysis is performed on the optimization model, and in each iteration, the stiffness matrix output by the data-driven model is used to calculate the sensitivity of the flexibility to the cutting height parameter, and the density output by the data-driven model is used to calculate the sensitivity of the volume fraction to the cutting height parameter, and the cutting height parameter is iteratively optimized according to the sensitivity to finally obtain the optimized dual-scale structure.

[0072] In some specific embodiments, S1 specifically includes:

[0073] For cells in the design domain of the dual-scale structure, multiple level set functions are selected, and multiple cutting operations are performed on each level set function to form multiple cutting height combinations. Each cutting height combination includes multiple cutting heights corresponding to the multiple level set functions. Multiple virtual microstructures corresponding to the multiple level set functions under each cutting height combination are obtained, and the multiple virtual microstructures are converted into density expressions and the max value is taken to obtain the density of the actual microstructure under each cutting height combination.

[0074] Correspondingly, the cutting height parameters in S2, S3 and S4 are cutting height combinations of multiple virtual microstructures. Multiple level set functions correspond to multiple virtual microstructures, each virtual microstructure corresponds to a cutting height, and multiple cutting heights of multiple virtual microstructures are combined to form a cutting height combination; under each cutting height combination, for any unit in the cell, the maximum density among the multiple virtual microstructures can be taken as the density of the actual microstructure of the unit, thereby obtaining the density of the actual microstructure of the cell.

[0075] See also Figure 1In this embodiment, the present invention is explained by taking the optimization problem of minimizing the flexibility of a plane cantilever beam structure with a concentrated load as an example. An initial dual-scale structure is set in a given 8m×4m rectangular design domain D, the left area of ​​the design domain is fixed, and a concentrated force F=1N is applied to the upper right corner area. The dual-scale structure is optimized to maximize its stiffness.

[0076] See also Figure 4 , this embodiment provides a dual-scale structural optimization design method based on substructure data driving, including:

[0077] Step 1: The cells in the design domain of the dual-scale structure are represented by the actual microstructure obtained by combination. In this embodiment, four level set functions are selected, that is, four virtual microstructures are corresponding to the cutting, and each group of cutting operations includes four cutting heights corresponding to the four virtual microstructures; each group of cutting operations is described by cutting a level set function with a horizontal cutting height, and the four virtual microstructures are converted into density expression and the max is taken to obtain the actual microstructure, and the actual microstructure finally obtained is used to describe the dual-scale structure.

[0078] Specifically, the given design domain D is divided into a certain number of square cells, the number of cells is 16×8; each cell includes multiple units, and the cell is the substructure of the dual-scale structure. Figure 2 As shown, the actual combined microstructure prototype Ω in each unit is obtained by taking the max value.

[0079] The S1 includes: cutting the virtual microstructure of the cell to a height h i k As the design variable, i=1, 2, ..., N, k is the number of cells, N is the number of virtual microstructures; combined with the design variable h i k Get the actual microstructure Ω of each cell k ; The overall dual-scale structure Ω is obtained using the actual microstructure.

[0080] The density of the actual microstructure in S1 is obtained according to the following formula:

[0081] Using the level set function and cutting height Represents the combined function obtained by a cutting operation

[0082]

[0083] Wherein, D is the design domain; k is the number of cells, M is the total number of cells, and N is the number of virtual microstructures;

[0084] The part where the combination function is less than 0 is defined as a virtual microstructure The part equal to 0 is defined as the boundary of the virtual microstructure, and the part greater than 0 is blank, and the virtual microstructure is obtained. for:

[0085]

[0086] Convert virtual microstructure into density results And perform the max operation to get the actual microstructure Ω k The density result ρ k :

[0087]

[0088] Finally, the actual microstructure is used to represent the dual-scale structure Ω:

[0089]

[0090] Step 2: The actual microstructure is obtained by statically condensing the units through the substructure method to obtain the stiffness matrix of the super unit under the cutting height combination, and a mapping model of the cutting height combination (including four cutting heights, corresponding to four virtual microstructures in this embodiment), the super unit stiffness matrix and the density of the actual microstructure is constructed.

[0091] Specifically, the stiffness matrix of the super element in S2 is obtained in the following way:

[0092] The finite element equilibrium equation of the substructure can be expressed as:

[0093] KU=F;

[0094] Among them, K is the global stiffness matrix; U is the global displacement vector; F is the global external force vector.

[0095] According to the finite element equilibrium equation of the substructure, the node degrees of freedom of the cell are first reordered according to the substructure method, and the appropriate node degrees of freedom are divided into internal node degrees of freedom and boundary node degrees of freedom. The finite element equilibrium equation of the cell is transformed into:

[0096]

[0097] Among them, K bb is the substructure stiffness matrix corresponding to the boundary node; K bi and K ib is the substructure stiffness matrix of the substructure boundary nodes and internal nodes coupled to each other; K ii is the substructure stiffness matrix corresponding to the internal nodes; U b is the displacement vector of the substructure boundary node; U i is the displacement vector of the node inside the substructure; Fb is the external force vector of the substructure boundary node; F i is the external force vector of the internal node of the substructure;

[0098] Then, the finite element equilibrium equation of the super-element is obtained by static condensation:

[0099] K r U r =F r ;

[0100] Since all selected external points are retained during the condensation process, namely U r =U b , we can get:

[0101]

[0102] Among them, K r is the stiffness matrix of the superelement; U r is the superelement displacement vector; F r is the superelement external force vector.

[0103] Specifically, Figure 3 As shown in the figure, 8 sets of corresponding data with a cutting height interval of 0.2 from -0.2 to 1.2 for each virtual microstructure are obtained by the substructure method, that is, each virtual microstructure is cut 8 times, and the cutting heights of the four virtual microstructures can be arbitrarily combined to obtain multiple sets of cutting height combinations, that is, the stiffness matrix of the corresponding super unit and the corresponding actual microstructure density as the offline database, where the database, that is, the mapping model, contains 8 4 There are 4096 super-element stiffness matrices and the density of the actual microstructure, i.e., the equivalent volume fraction.

[0104] Step 3, using the compact support radial basis function interpolation technology to interpolate the mapping model to obtain a data-driven model with the virtual microstructure cutting height as input and the super-element stiffness matrix and the density of the actual microstructure as output. That is, S3 specifically includes: using the compact support radial basis function interpolation technology to interpolate the mapping model to obtain the data-driven model.

[0105] Specifically, the stiffness matrix of the super-element and the density of the actual microstructure are obtained by using the compact support radial basis function interpolation formula and the mapping model as follows:

[0106]

[0107] Among them, K m H is the stiffness matrix obtained by interpolation; i = 1…N, N is the number of virtual microstructures; n is the number of node degrees of freedom of the super-element after condensation; V His the volume obtained by interpolation; α is the expansion coefficient of the compactly supported radial basis function; φ(r) is the radial basis function; r is the distance from the interpolation point to the center point; p i represents the coordinate center point of the interpolation function; x here represents the cutting height combination of various virtual microstructures in the cell; τ is the free shape parameter; d s A custom constant.

[0108] Specifically, the reference points for interpolation are the points before and after the closest cutting height in each microstructure, that is, interpolation is performed at 8 points. The parameters n in the compact support radial basis function are 320, τ is 0.05, d s is 2. Here m is the degree of freedom of the superelement node after condensation, which is 102400.

[0109] Step 4: Use the substructure data-driven model for dual-scale structure optimization design: take the four groups of cutting heights in each cell in the dual-scale design domain, i.e., cutting height combinations, as design variables, and the volume fraction of the dual-scale structure as a constraint condition, and obtain the optimization result with the minimum flexibility of the dual-scale structure as the objective function;

[0110] Specifically, the optimization model described in S4 is:

[0111]

[0112] Where i represents the type of virtual microstructure; c is the flexibility; V is the volume; is the volume value of the constraint; U is the global displacement vector; F is the global external force vector, which is a preset value. i=4.

[0113] The optimized dual-scale structure in S4 specifically includes:

[0114] Finite element analysis is performed on the optimization model to calculate the sensitivity of flexibility to the cutting height combination, the sensitivity of volume fraction to the cutting height combination, and the moving asymptote method is used to update the cutting height combination;

[0115] When the updated structural flexibility error meets the preset optimization termination condition, the optimization analysis is completed and the optimized dual-scale structure is obtained.

[0116] That is, the present embodiment also includes step 5, performing finite element analysis, calculating the sensitivity of flexibility to cutting height, calculating the sensitivity of volume fraction to cutting height, and updating the cutting height using the moving asymptote method (MMA); specifically, according to the objective function, the constraint function, and the sensitivity of the objective function and the constraint function to the design variables, the design variable h is updated in combination with the moving asymptote method (MMA). i, MMA is an existing optimization algorithm, which will not be described here. inew The distribution of the actual microstructure in each cell is represented to obtain the overall dual-scale structure.

[0117] Among them, the sensitivity of flexibility to the cutting height combination can be expressed as:

[0118]

[0119] Among them, using the Substitute the formula KU=F to solve the overall displacement vector U, where F is the external force vector; and according to the compact support radial basis function interpolation formula, we can It is expressed as:

[0120]

[0121] The sensitivity of volume fraction to the combination of cut heights is expressed as:

[0122]

[0123] According to the structural relationship of the microstructure, we can get:

[0124]

[0125] Where V is the volume of the dual-scale structure; ρ k is the density of the actual microstructure corresponding to the kth cell; M is the total number of cells.

[0126] Step six: when the updated structural flexibility error meets the optimization termination condition, the optimization analysis is completed and a dual-scale structure that meets the requirements is obtained, otherwise, return to step five.

[0127] Specifically, each repetition is called an iteration until the optimization termination condition is met and the optimal design of the dual-scale structure is obtained. The optimization termination condition is set as

[0128]

[0129] where c err is the flexibility error, k is the current iteration number, ε is the lower limit of the flexibility error, which is 0.1% here, k max is the upper limit of the number of iterations, which is 1000 here.

[0130] The optimization results of this preferred embodiment are as follows:

[0131] The optimized dual-scale structure is as follows Figure 5 As shown, the compliance value is 151.40. The optimized dual-scale structure ensures the connectivity between microstructures and obtains the best material distribution.

[0132] The second embodiment of the present invention provides a dual-scale structure optimization design system based on substructure data drive, the system includes a memory and a processor, the memory stores a computer program, and the processor executes any of the above-mentioned dual-scale structure optimization design methods based on substructure data drive when executing the computer program.

[0133] The invention discloses a dual-scale structure optimization design method based on substructure data drive, the design method includes an offline part and an online part; the offline part includes: defining the design domain of the dual-scale structure, each cell in the design domain is formed by forming a virtual microstructure obtained by cutting a level set function into an actual microstructure, specifying different cutting heights to obtain a series of microstructures that change with the cutting height; obtaining the corresponding super-element stiffness matrix according to the density of the microstructure by a static condensation method, storing a database containing multiple sets of super-element stiffness matrices and densities; constructing a mapping model about the virtual microstructure cutting height, super-element stiffness matrix and actual microstructure density. The online part includes: taking the cutting height of the microstructure as a design variable, using radial basis function interpolation to obtain the density and stiffness matrix of the actual microstructure under the required design variable to form a data-driven model, using the data-driven model for finite element analysis and sensitivity analysis, iterating repeatedly until the optimization termination condition is met, and obtaining the optimal dual-scale structure. The design method improves the computational efficiency while ensuring the connectivity of the microstructure in a data-driven manner.

[0134] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A dual-scale structural optimization design method based on substructure data drive, characterized in that: include: Offline data processing stage: S1, for the cells in the design domain of the dual-scale structure, the virtual microstructure is obtained by cutting the level set function, the density of the actual microstructure is determined according to the density of the virtual microstructure, and the dual-scale structure is described by the actual microstructure; S2, according to the density of the actual microstructure of the cell, static condensation is performed through the substructure method to obtain the stiffness matrix of the super unit formed after the cell is condensed, and a mapping model of the cutting height parameter in the cutting operation, the stiffness matrix of the super unit and the density of the actual microstructure is constructed; Online optimization design stage: S3, obtaining a data-driven model with a cutting height parameter as an input quantity and a stiffness matrix of a super-element and a density of an actual microstructure as an output quantity according to the mapping model; S4, taking the cutting height parameters of each cell in the design domain of the dual-scale structure as the design variables, the volume fraction as the constraint condition, and the minimum flexibility as the objective function, an optimization model of the dual-scale structure is established; finite element analysis is performed on the optimization model, and in each iteration, the stiffness matrix output by the data-driven model is used to calculate the sensitivity of the flexibility to the cutting height parameter, and the density output by the data-driven model is used to calculate the sensitivity of the volume fraction to the cutting height parameter, and the cutting height parameter is iteratively optimized according to the sensitivity to finally obtain the optimized dual-scale structure.

2. The dual-scale structural optimization design method based on substructure data drive according to claim 1, characterized in that: S1 specifically includes: For cells in the design domain of the dual-scale structure, multiple level set functions are selected, and multiple cutting operations are performed on each level set function to form multiple cutting height combinations. Each cutting height combination includes multiple cutting heights corresponding to the multiple level set functions. Multiple virtual microstructures corresponding to the multiple level set functions under each cutting height combination are obtained, and the multiple virtual microstructures are converted into density expressions and the max value is taken to obtain the density of the actual microstructure under each cutting height combination. Correspondingly, the cutting height parameters in S2, S3 and S4 are cutting height combinations of various virtual microstructures.

3. The substructure data-driven dual-scale structural optimization design method according to claim 2, characterized in that: The density of the actual microstructure in S1 is obtained according to the following formula: Using the level set function and cutting height Represents the combined function obtained by a cutting operation Wherein, D is the design domain; k is the number of cells, M is the total number of cells, and N is the number of virtual microstructures; The part where the combination function is less than 0 is defined as a virtual microstructure Get virtual microstructure for: Convert virtual microstructure into density results And perform the max operation to get the actual microstructure Ω k The density result ρ k : Finally, the actual microstructure is used to represent the dual-scale structure Ω:

4. The substructure data-driven dual-scale structural optimization design method according to claim 1, characterized in that: The stiffness matrix of the super element in S2 is obtained in the following way: First, according to the substructure method, the node degrees of freedom of the cell are reordered, and the appropriate node degrees of freedom are divided into internal node degrees of freedom and boundary node degrees of freedom. The finite element equilibrium equation of the cell is transformed into: Among them, K bb is the substructure stiffness matrix corresponding to the boundary node; K bi and K ib is the substructure stiffness matrix of the substructure boundary nodes and internal nodes coupled to each other; K ii is the substructure stiffness matrix corresponding to the internal nodes; U b is the displacement vector of the substructure boundary node; U i is the displacement vector of the node inside the substructure; F b is the external force vector of the substructure boundary node; F i is the external force vector of the internal node of the substructure; Then, the finite element equilibrium equation of the super-element is obtained by static condensation: K r U r =F r ; Since all selected external points are retained during the condensation process, namely U r =U b , we can get: Among them, K r is the stiffness matrix of the superelement; U r is the superelement displacement vector; F r is the superelement external force vector.

5. The dual-scale structural optimization design method based on substructure data drive according to claim 2, characterized in that: S3 specifically includes: The mapping model is interpolated using a compactly supported radial basis function interpolation technique to obtain the data driven model.

6. The substructure data-driven dual-scale structural optimization design method according to claim 5, characterized in that: The stiffness matrix of the super-element and the density of the actual microstructure are obtained by using the compact support radial basis function interpolation formula and the mapping model as follows: in, is the stiffness matrix obtained by interpolation; i = 1…N, N is the number of virtual microstructures; n is the number of node degrees of freedom of the super-element after condensation; V H is the volume obtained by interpolation; α is the expansion coefficient of the compactly supported radial basis function; φ(r) is the radial basis function; r is the distance from the interpolation point to the center point; p i represents the coordinate center point of the interpolation function; x here represents the cutting height combination of various virtual microstructures in the cell; τ is the free shape parameter; d s A custom constant.

7. The substructure data-driven dual-scale structural optimization design method according to claim 6, characterized in that: The optimization model described in S4 is specifically: Where i represents the type of virtual microstructure; c is the flexibility; V is the volume; is the volume value of the constraint; U is the global displacement vector; F is the global external force vector.

8. The substructure data-driven dual-scale structural optimization design method according to claim 7, characterized in that: The sensitivity of compliance to the combination of cutting heights can be expressed as: According to the compactly supported radial basis function interpolation formula, we can It is expressed as: The sensitivity of volume fraction to the combination of cut heights is expressed as: Where V is the volume of the dual-scale structure; ρ k is the density of the actual microstructure corresponding to the kth cell; M is the total number of cells.

9. The substructure data-driven dual-scale structural optimization design method according to claim 2, characterized in that: The optimized dual-scale structure in S4 specifically includes: Finite element analysis is performed on the optimization model to calculate the sensitivity of flexibility to the cutting height combination, the sensitivity of volume fraction to the cutting height combination, and the moving asymptote method is used to update the cutting height combination; When the updated structural flexibility error meets the preset optimization termination condition, the optimization analysis is completed and the optimized dual-scale structure is obtained.

10. A dual-scale structural optimization design system driven by substructure data, characterized in that: The system includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the substructure data-driven dual-scale structure optimization design method described in any one of claims 1 to 9 is executed.

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